Exact solution of the Boltzmann equation in the homogeneous color conductivity problem

An exact solution of the Boltzmann equation for a binary mixture of colored Maxwell molecules is found. The solution corresponds to a nonequilibrium homogeneous steady state created by a nonconservative external force. Explicit expressions for the moments of the distribution function are obtained. By using information theory, an approximate velocity distribution function is constructed, which is exact in the limits of small and large field strengths. Comparison is made between the exact energy flux and the one obtained from the information theory distribution.     

Exact solution of the non-linear Boltzmann equation for Maxwell models

The exact solution of the Boltzmann equation, obtained recently for Maxwell molecules, holds for various models with arbitrary dimensionality. Furthermore, simple non-linear equations are derived for the ordinary and the Sonine moments, which can be solved subsequentially.     

Exact moment solution of the Boltzmann equation for uniform shear flow

The Ikenberry-Truesdell exact solution to the Boltzmann equation for Maxwell molecules is revisited. This solution refers to a state characterized by a linear profile of the velocity flow and spatially uniform density and temperature. The solution is extended to include explicit expressions for the fourth-degree moments. It is shown that if the shear rate is larger than a certain critical value, the fourth-degree moments do not reach stationary values, even when the temperature is kept constant. The explicit shear-rate dependence of the moments below this critical value are obtained.     

On the three-term approximation of the solution of the Boltzmann equation for weakly ionized gases

In this paper we discuss an improvement of the current technique of solution of the Boltzmann equation for weakly ionized gases in an electric field. The method is based on the usual expansion of the velocity distribution in spherical harmonics, but three terms of the expansion are retained instead of two. In the light of the results obtained for a particular interaction law between charged and neutral particles, a procedure is established which is consistent in the orders of approximation. This procedure requires an improvement of the degree of accuracy commonly used for the terms deriving from the Boltzmann collision operator. For this reason, the general expression of the isotropic collision operator correct to second order in the ion-neutral mass ratio is calculated. Finally, a new steady-state solution of the Boltzmann equation is obtained which is valid both for electrons and light ions in heavy gases.     

Global existence in L1 for the Enskog equation and convergence of the solutions to solutions of the Boltzmann equation

For the Enskog equation in a box an existence theorem is proved for initial data with finite mass, energy, and entropy. Then, by letting the diameter of the molecules go to zero, the weak convergence of solutions of the Enskog equation to solutions of the Boltzmann equation is proved.     

Some remarks about continuity properties of local Maxwellians and an existence theorem for the BGK model of the Boltzmann equation

Continuity of local Maxwellians in various topologies ofL ¹ is studied. The existence and convergence of approximate solutions of the nonlinear BGK model of the Boltzmann equation are proved.     

Internal field relaxation and its effect on the energy spectrum and transport characteristics of a quantum well

We consider internal field relaxation and its effect on the transport characteristics (transmission probability) and the energy spectrum of a quantum well in the context of a modified transfer matrix method. It is shown that the internal field relaxation process leads to the expulsion of the bound state from a quantum well, and to a change in the transport characteristics of such a structure.     

Deconvolution of temperature dependence of conductivity,its reduced activation energy,and Hall-effect data for analysing impurity conduction in n-ZnSe

ABSTRACT

The temperature dependence of the reduced activation energy w?=?ε/k_BT of the conductivity σ has been utilised for determining the impurity conduction mechanism in doped semiconductors in many studies. Herein, the formula for deconvoluting w when plural conduction mechanisms appear is used to confirm the analysis of the data of the Hall-effect measurements on Al-doped n-ZnSe samples. The analysis is performed on the basis of an impurity-Hubbard-band model which includes ε ₂ conduction in the top Hubbard band as well as ε ₃ and Efros-Shklovskii (ES) variable-range hopping (VRH) conduction processes in the bottom Hubbard band. As the result of the analysis, transitions among the three hopping conduction mechanisms of ε ₂, ε ₃, and ES VRH are clearly shown in the temperature dependence of w as well as in that of the Hall mobility, which are hardly noticed in the temperature dependence of σ. In addition, the power-law exponent of the prefactor of ES VRH conductivity is determined through the fit to the temperature dependence of w to show that it decreases from ～ 1.5 to ～ 0 with increasing net donor concentration.     

弹性矩形板方程在非线性边界条件下整体解的存在唯一性

考虑了在非线性边界条件下的弹性矩形板方程.利用Galerkin方法,首先证明了该方程在非线性边界(a)及初值w⁰∈W,w¹∈W的条件下初边值问题存在唯一整体弱解w(t).其次证明了该方程在非线性边界(b)及初值w⁰∈W₁,w¹∈W₁的条件 关键词： 弹性矩形板方程 非线性边界条件 初边值问题 整体解     

Calculating the intensities of absorption bands of the IR spectrum for benzylidene methylamine and its deuteroanalogs

To whom correspondence should be addressd.     

Exact solution to the classical equation of motion for a charged particle in external electric and magnetic fields

An exact solution to the equation of classical motion of a charged particle in external uniform time-dependent electric and magnetic fields is obtained in two forms by two methods. An exact solution of a more general initial-value problem is found as well.     

An approximation for rotation-projected expectation values of the energy for deformed nuclei and a derivation of the cranking variational equation

An approximation is given for the expectation value of the Hamiltonian with functions: where ¦?〉 is a HFB wave function of a deformed nucleus. This is achieved by expanding the overlap function of the energy 〈?¦ HD(Ω)¦?〉 in derivatives of the overlap function of the norm 〈? D(Ω)¦?〉. The cranking equations for even nuclei are yielded by varying the approximate energy.     

Experimental energy bands,exchange splittings,and lifetimes for Ni in the vicinity of the x-point

Angle-resolved photoelectron spectroscopy using synchrotron radiation has been used to determine energy band dispersions along the ΓKX and ΓX directions in nickel. A detailed picture of spin-dependent energy levels and band topology around the symmetry point X has been derived. We have measured the exchange splitting for different band symmetries and find the splitting for the X₂-S₄ band along (110) to be 0.17 eV. For the X₅-S₃ band we find a splitting of 0.33 eV which is in close agreement with the value found earlier for the Σ₂ band. This can be explained by different self-energy corrections for t_2g and e_g-type states respectively. Our values for the energy positions (inverse lifetimes) are the following: X_2↓ = ?0.04 eV (0.08 eV, X_2↑ = ?0.24 eV (0.19 eV), X_5↑ = ?0.11 eV.     

3ω法加热/测温膜中温度波解析及其在微/纳米薄膜导热系数测量中的应用

给出了3ω法测试系统中描述薄膜表面加热/测温膜中温度波动的级数形式解，并将复数温度波动的实部和虚部分开表示.利用该解分析了交流加热频率、加热膜宽度和材料热物性的组合参数对加热膜温度波动幅度的影响.并根据此解对测量原理的数学模型进行了修正，建立了相应的3ω测试系统，首先测定了厚度为500 nm SiO₂薄膜的导热系数，验证了实验系统的合理性.加大了测试频率，利用级数模型在高频段直接得到SiO₂薄膜的导热系数，结合低频段的数据同时确定了Si基体的导热系数.利用级数解分析测试了激光晶体Nd:YAG〈111〉面上多层ZrO₂/SiO₂增透膜的导热系数，测试的ZrO₂薄膜的导热系数比体材料小.进行了不确定度分析.结果表明，提出的分析方法可以有效研究微器件表面薄膜结构的导热性能. 关键词： ω法')" href="#">3ω法 微/纳米薄膜 导热系数 微尺度加热膜     

Calculation of the charge-carrier relaxation time, Hall factor, and differential thermal EMF for isotropic p-type polysilicon

A model of an isotropic polycrystal is considered. An approach based on the solution to the kinetic Boltzmann equation is proposed for calculation of the charge-carrier relaxation time at the potential barriers formed on the surfaces of crystallites in the p-type polysilicon. The Hall factor for charge-carrier scattering by these barriers in a weak magnetic field and the differential thermal EMF resulting from the hole scattering by the potential barriers formed on the crystallite surface are calculated. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 87–96, July, 2006.     

Exact analytical solution for the vector electromagnetic field of Gaussian, flattened Gaussian, and annular Gaussian laser modes

The exact vector integral solution for all the electromagnetic field components of a general flattened Gaussian laser mode is derived by using the angular spectrum method. This solution includes the pure and annular Gaussian modes as special cases. The integrals are of the form of Gegenbauer's finite integral and are computed analytically for each case, yielding fields satisfying the Maxwell equations exactly in the form of quickly converging Fourier-Gegenbauer series.     

The solution of the kinetic equation for phonon heat conductivity by the method of momenta and the influence of isotopic disorder on phonon heat conductivity of germanium and silicon crystals at T=300 K

The problem of solving the kinetic equation for the heat conductivities of dielectric substances and semiconductors by the method of momenta is discussed. Microscopic models are used to estimate the effect of isotopic disorder on the thermal resistance of germanium crystals in the multimomentum approximation. The contributions of acoustic and optical phonons are taken into account. Excess thermal resistance ΔW of samples with a natural isotopic composition compared with highly enriched samples is calculated. For germanium, the theoretical and experimental Δ W values are in close agreement with each other. For silicon, the theoretical ΔWvalue is much smaller than its experimental excess thermal resistance.     

Influence of temperature on the electric,dielectric and AC conductivity properties of nano-crystalline zinc substituted cobalt ferrite synthesized by solution combustion technique

Cobalt–zinc nanoferrites with formulae Co $_{1-x}$ Zn $_{x}$ Fe $_{2}$ O $_{4}$ , where x = 0.0, 0.1, 0.2 and 0.3, have been synthesized by solution combustion technique. The variation of DC resistivity with temperature shows the semiconducting behavior of all nanoferrites. The dielectric properties such as dielectric constant ( $\varepsilon $ ’) and dielectric loss tangent (tan $\delta )$ are investigated as a function of temperature and frequency. Dielectric constant and loss tangent are found to be increasing with an increase in temperature while with an increase in frequency both, $\varepsilon $ ’ and tan $\delta $ , are found to be decreasing. The dielectric properties have been explained on the basis of space charge polarization according to Maxwell–Wagner’s two-layer model and the hopping of charge between Fe $^{2+}$ and Fe $^{3+}$ . Further, a very high value of dielectric constant and a low value of tan $\delta $ are the prime achievements of the present work. The AC electrical conductivity ( $\sigma _\mathrm{AC})$ is studied as a function of temperature as well as frequency and $\sigma _\mathrm{AC}$ is observed to be increasing with the increase in temperature and frequency.